Just as in every world tradition, there is a heart teaching or esoteric aspect of Islam. The most widely known is the Sufi tradition, and the brilliant mystical poet Rumi.

Let the body needs dwindle and the sould decisions increase.
Diminish what you give your physical self.
Your spiritual eye will open.

[...]

Listen to the prophets, not to some adolescent boy.
The foundation and the walls of the spiritual life
are made of self-denials and disciplines.
-Rumi, Muhammed and the Huge Eater